Or have different ranges for different types (personally I think it would be good to get more combat occurring onscreen rather than at the edge of the LRS) e.g.
Beams: short range (< screen)
Bullets: medium (~screen)
Missiles: long range (> screen)

If anything, I like to be able to zoom the SRS screen out and see more long-range combat. Other games I play (Endless Sky one of them) seem to have a fetish for short-range combat, which gets annoying at times. Overuse of short-range combat feels more like hack-and-slash instead of a shooting game. Fortunately, Transcendence avoids excessive short-range combat.

I definitely like that idea. Restricting fast, accurate weapons like lasers to short range, letting bullets be more difficult to use but longer ranged, and (most importantly) making the highest ranged weapons ammo - based or in possession of other significant drawbacks is a good balancing strategy. Lancers were OP in early versions because they had high damage, accuracy, and range. Howitzers, with their high(and more upgradeable than any other lategame weapon) damage, high accuracy, high range, and WMD take this role now. Missiles, on the other hand, seem to get the worst of all worlds, being expensive to use, shorter ranged, and roughly as lethal as moderately upgraded howitzers.

If anything, I like to be able to zoom the SRS screen out and see more long-range combat. Other games I play (Endless Sky one of them) seem to have a fetish for short-range combat, which gets annoying at times. Overuse of short-range combat feels more like hack-and-slash instead of a shooting game. Fortunately, Transcendence avoids excessive short-range combat.

Being able to zoom the SRS screen so combat was on screen would indeed get the combat to occur onscreen.

Scale the screen to fit what is happening, or scale what is happening to fit the (average) screen...

Screen scaling is an advantage Endless Sky has over Transcendence, and since Endless Sky recently implemented their version of autopilot (3x instead of 5x) in 0.9.7, I zoom the screen out more because the time shift offsets slowdown from whatever reason and/or give me more time to react to incoming hostiles while fighting at faster-than-normal speed.

Screen scaling is an advantage Endless Sky has over Transcendence, and since Endless Sky recently implemented their version of autopilot (3x instead of 5x) in 0.9.7, I zoom the screen out more because the time shift offsets slowdown from whatever reason and/or give me more time to react to incoming hostiles while fighting at faster-than-normal speed.

I think they use vector images. Much easier to scale those and not look terrible.

Some games have continuous beams that are not hitscan, but they are always continuous in that if the source rotates, so does the entire beam. I have recreated that effect with a quick small mod. The entire mod is in the code block below. It overwrites the dual laser cannon so that all the player needs to do to play is select the Wolfen. I have not tried to balance the so-called guided laser.

Perhaps something like this could be a way to have continuous beams without them being at relativistic speeds. It also has the side-effect of distance affecting DPS.

For the example mod I posted, I overlooked that missileSpeed of 100 and lifetime of 1 means AI will only shoot at targets up to range 2, meaning it will almost never shoot at all! That can be fixed by putting range into missileSpeed and adjusting the OnFireWeapon event to account for that. AI will still aim badly (if no further corrective code is added) because it assumes relativistic shot, but at least it will shoot.

Aside from the above...

If guided beam has same missile speed as normal beams, then for it to have decent range, it needs to fire the beam for many frames, and for such a weapon to balanced, it needs a long fireRate. Swapping to a weapon that fires much slower than once every two seconds is painful to use as a primary weapon because as soon as the player switches to the weapon, he needs to wait as long as the reload delay before he can fire. It is less problematic as a launcher (and I may add a few mod ammoless launchers that shoot guided beams.)

Also, omnidirectional beam that fires for many frames should update aim so that much of the beam does not miss a moving target. Updating aim during a burst requires custom code.

Finally, if player wants such a weapon to fire continuously as long as the fire button is held, then when the weapon was last fired needs to be tracked somehow. (For that, I probably would use charges to store (unvGetTick), and that makes things a bit more messy.)

Here is take two on guided (or non-relativistic continuous) beams. This should be usable on playerships and NPC ships (and stations) alike. The only limitation is the item relies on charges. The mini-mod code below replaces laser cannon and the dual and Omni variants. Just select either EI500 or Wolfen to play with them. If you want to see them used against you, pick a fight with Corsairs or Hornets.